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Excursion and contour uncertainty regions for latent Gaussian models
Author(s) -
Bolin David,
Lindgren Finn
Publication year - 2015
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12055
Subject(s) - excursion , gaussian , parametric statistics , geostatistics , gaussian process , set (abstract data type) , computer science , algorithm , data set , sampling (signal processing) , mathematics , ranging , statistics , artificial intelligence , computer vision , spatial variability , telecommunications , physics , filter (signal processing) , quantum mechanics , political science , law , programming language
Summary In several areas of application ranging from brain imaging to astrophysics and geostatistics, an important statistical problem is to find regions where the process studied exceeds a certain level. Estimating such regions so that the probability for exceeding the level in the entire set is equal to some predefined value is a difficult problem connected to the problem of multiple significance testing. In this work, a method for solving this problem, as well as the related problem of finding credible regions for contour curves, for latent Gaussian models is proposed. The method is based on using a parametric family for the excursion sets in combination with a sequential importance sampling method for estimating joint probabilities. The accuracy of the method is investigated by using simulated data and an environmental application is presented.